few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Create equations that describe numbers or relationships

Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.

Analyze patterns and relationships.

Multiply and divide within 100.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Represent and solve problems involving multiplication and division.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand and apply properties of operations and the relationship between addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Generate and analyze patterns.

Gain familiarity with factors and multiples.

Write expressions in equivalent forms to solve problems.

Understand the connections between proportional relationships, lines, and linear equations.

Use the four operations with whole numbers to solve problems.

Represent and solve equations and inequalities graphically.

Understand properties of multiplication and the relationship between multiplication and division.

Write and interpret numerical expressions.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent and analyze quantitative relationships between dependent and independent variables.

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Use polynomial identities to solve problems.

Understand solving equations as a process of reasoning and explain the reasoning.

Solve equations and inequalities in one variable.

Work with radicals and integer exponents.

Work with equal groups of objects to gain foundations for multiplication.

Rewrite rational expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.
problem_activity: Narrative
The purpose of this activity is for students to find the value of quotients where the divisor is less than 1 and where the dividend is large enough that drawing a complete diagram is cumbersome. Instead, students are encouraged to use a diagram to find
how many divisor sized groups are in 1 whole and then multiply the dividend by that number to find the value of the quotient. When students use the value of
\(1 \div 0.2\)
and multiplication to find the value of
\(12 \div 0.2\)
they are using regularity in reasoning (MP8).
This activity uses
MLR1 Stronger and Clearer Each Time.
Advances: Conversing.
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including the tools they will use, for finding the value of the expression. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Copy
Small Grids
Launch
Groups of 2
Give students access to blackline masters with hundredths grids.
Activity
3–5 minutes: independent work time
Monitor for students who use the following strategies for problem 1:
reason about how many divisor-sized groups are in 1 whole, possibly with a diagram, and then multiply by the dividend
use multiplication equations to find the value of the division expressions
Student Facing
Find the value of the expression. Use a diagram if it is helpful.
\(12 \div 0.2\)
[IMG]
This is the diagram and explanation Tyler used to justify why
\(12 \div 0.2 = 60\)
.
[IMG]
[IMG]
Explain how the expression
\(12 \times (1 \div 0.2)\)
relates to Tyler's reasoning.
Find the value of each expression.
\(14 \div 0.5\)
\(5 \div 0.25\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If a student is not sure how to explain Tyler’s reasoning in problem 2, ask them to read the expression to you and record the words they use. Then ask them how those words relate to the words Tyler used.
Activity Synthesis
Ask previously identified students to share their solutions and strategies for evaluating the expression in the first problem.
“How was multiplication useful to find the value of the expression in the first problem?” (I didn't have to draw 12 wholes because I knew there were five 0.2s in each one so that would be
\(12 \times 5\)
total.)
MLR1 Stronger and Clearer Each Time
“Share your response to problem 2 with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3-5 minutes: structured partner discussion
Repeat with 2 different partners.
“Revise your initial draft based on the feedback you got from your partners.”
2-3 minutes: independent work time


correct_option_index: 19